For much of the affair, “Stan & Ollie” — a portrait of a specific time in the lives and careers of famed comedy duo Stan Laurel and Oliver Hardy — feels a little tired, perhaps too much like the seemingly past-their-primes comedians who are its focus.

But when this classic bromance — “It’s a love story,” screenwriter Jeff Pope says in the film’s production notes — concludes, it does it in such a touching way that it improves upon all that has come before these final moments.

And thus it becomes easier to recommend “Stan & Ollie,” bolstered by a solid performance as Steve Coogan as Stan and a more memorable turn by John C. Reilly as Ollie, than you think it may be while watching its first half or so.

Directed by Jon S. Baird, “Stan & Ollie” begins in the 1930s, with an impressive tracking shot that follows the prolific duo — the aforementioned notes credit them with more than 100 film appearances, including shorts and features, both silent and with sound, from 1927 to 1950 — from their dressing room, through the studio lot and finally onto a movie set to film a scene.

Along the way, they argue with studio boss Hal Roach (Danny Huston) over their contracts. While both believe they deserve more money — that they should be making similar to what contemporaries such as Charlie Chaplin and Buster Keaton are, even while acknowledging their situations are different from that of those men — Stan is more eager to go to war with Hal over the issue. Complicating matters is that Stan’s contract with the studio will be up soon, while Ollie is locked in for a longer stretch.

During this, the film’s prologue, Pope and Baird give us a good feel for the dynamic of Stan and Ollie, who, more are less, are doing bits in their private moments. One such exchange occurs after Ollie, aka “Babe,” updates Stan on his money troubles connected to his ex-wives and his gambling habit.

“Lay off the horses and don’t get married again,” Stan advises his partner.

“Oh, I didn’t tell you,” Ollie replies, “I proposed to Lucille.”

Stan congratulates them and adds that he is never getting married again — that he’ll save himself some trouble by simply finding a woman he doesn’t like and buy her a house.

“That’s a good one,” Ollie replies.

We then skip ahead about a decade and a half, long past a split starting with Stan leaving the studio and Ollie agreeing to do a picture with another actor. We now have a reunited Laurel and Hardy going on a theater tour in England in the hopes of making a little scratch but also in generating enough buzz to where a film producer will greenlight a Robin Hood film Stan has been writing for the two of them.

The two men are getting along, but there is much more baggage between them than the luggage they carry from one unimpressive hotel to another. Plus, each has a wife back at home — Ollie’s Lucille (Shirley Henderson) and Stan’s Ida (Nina Arianda) — primarily concerned with her man’s best interests. (Things do not become easier for the husbands when the wives visit and no longer can be kept at bay with brief phone calls.)

The magic still exists between Stan and Ollie, especially on stage, where they perform before enthusiastic but frustratingly small audiences. If things don’t improve, the gregarious but box office-focused tour producer (an enjoyable Rufus Jones) will pull the plug before the endeavor can get to London — and in front of the eyes of the all-important movie producer.

While the men agree to do more publicity stunts for the show and see buzz for their performances grow tremendously as a result, it may not be enough. Plus, the overweight Ollie is dealing with health concerns, starting with knee pain that makes much of their signature physical comedy difficult. (By the 1950s, the production notes say, Hardy weighed nearly 400 pounds, and Reilly sat in a makeup chair for four hours and wore a fat suit for the role. The results are excellent, by the way — without this information, a viewer may wonder if Reilly actually gained a dangerous amount of weight for the film.)

While you wish Baird had injected the film with a bit more energy, Coogan (“Philomena,” “Night at the Museum”) and Reilly (“Step Brothers,” “Gangs of New York”) are increasingly fun to watch together, performing as Laurel and Hardy whether for an audience or by themselves. In fact, perhaps the best aspects of the script by Pope (“Philomena”) is his portrayal of their dynamic in private. Stan comes up with the ideas for their gags, and Ollie sits in complete appreciation during Stan’s pitches, occasionally offering a tweak to the idea but typically simply laughing at it with obvious sincerity.

While “Stan & Ollie” has its mildly dull stretches, it boasts an undeniable old-fashioned charm, and the guess here is it will delight longtime fans of Laurel and Hardy.